Line a small baking sheet with parchment paper. Set aside.
Using a fork, in a small bowl, combine the goat cheese and basil until smooth. Season with salt and pepper, to taste. Using a 1/2-ounce cookie scoop or a round tablespoon measure sprayed with vegetable oil cooking spray, scoop the goat cheese into balls and arrange on the prepared baking sheet. Refrigerate for 30 minutes.
In a Dutch oven or large saucepan, heat the butter over medium heat. Add the leeks and cook, stirring constantly until softened, about 3 to 4 minutes. Add the broth, asparagus and basil. Season with salt and pepper, to taste. Increase the heat to high and bring the mixture to a boil. Reduce to a simmer and cook until the asparagus is tender, about 15 minutes. Using an immersion blender, blend the soup until smooth. Season with salt and pepper, to taste. Keep the soup warm over low heat.
Ladle the soup into shallow bowls and garnish with the herbed goat cheese.
The soup can also be pureed by ladling, in batches, into a food processor or blender and blended until smooth.